A359690
Number of vertices in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n.
Original entry on oeis.org
5, 13, 69, 289, 1971, 3997, 20371, 45751, 120957, 205299, 629847, 897801, 2334409, 3461459, 5517131, 8468061
Offset: 1
Cf.
A359691 (crossings),
A359692 (regions),
A359693 (edges),
A359694 (k-gons),
A005728,
A331755,
A359654,
A358887,
A358883,
A006842,
A006843.
A359694
Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n.
Original entry on oeis.org
2, 10, 2, 70, 24, 218, 160, 4, 1254, 1068, 148, 16, 2254, 2414, 252, 26, 10082, 11760, 1980, 266, 12, 21410, 25958, 5096, 648, 36, 4, 53422, 68208, 14360, 1980, 168, 20, 86986, 118922, 24028, 3056, 248, 12, 0, 2, 255678, 346676, 84344, 12774, 1132, 110, 4, 2, 365674, 493530, 119820, 18600, 1624, 112, 4
Offset: 1
The table begins:
2;
10, 2;
70, 24;
218, 160, 4;
1254, 1068, 148, 16;
2254, 2414, 252, 26;
10082, 11760, 1980, 266, 12;
21410, 25958, 5096, 648, 36, 4;
53422, 68208, 14360, 1980, 168, 20;
86986, 118922, 24028, 3056, 248, 12, 0, 2;
255678, 346676, 84344, 12774, 1132, 110, 4, 2;
365674, 493530, 119820, 18600, 1624, 112, 4;
917478, 1244492, 334096, 57080, 5700, 478, 16, 4;
1335398, 1862666, 495536, 82642, 8096, 676, 24, 6;
2107042, 2989864, 788340, 128378, 12536, 932, 52, 4;
3195474, 4557430, 1230300, 205352, 20516, 1664, 80, 4;
.
.
Cf.
A359690 (vertices),
A359691 (crossings),
A359692 (regions),
A359693 (edges),
A005728,
A290131,
A359653,
A358886,
A358882,
A006842,
A006843.
A359692
Number of regions in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n.
Original entry on oeis.org
2, 12, 94, 382, 2486, 4946, 24100, 53152, 138158, 233254, 700720, 999364, 2559344, 3785044, 6027148, 9210820
Offset: 1
Cf.
A359690 (vertices),
A359691 (crossings),
A359693 (edges),
A359694 (k-gons),
A005728,
A290131,
A359653,
A358886,
A358882,
A006842,
A006843.
A359970
Number of edges formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions equal the Farey series of order n.
Original entry on oeis.org
3, 10, 84, 433, 3264, 7357, 37065, 86441, 232975, 405510, 1210898, 1773121, 4500787, 6774404, 10997356
Offset: 1
A359976
Number of edges formed inside a right triangle by the straight line segments mutually connecting all vertices and points on the two shorter edges whose positions on one edge equal the Farey series of order n while on the other they divide its length into n equal segments.
Original entry on oeis.org
3, 10, 55, 202, 902, 1868, 5886, 11676, 24322, 39440, 84155, 120151, 228121, 324856, 474396, 670552, 1104433, 1402237, 2185044, 2761367, 3654893, 4628608, 6706612, 8005739, 10770733
Offset: 1
- McIlroy, M. D. "A Note on Discrete Representation of Lines". AT&T Technical Journal, 64 (1985), 481-490.
A359691
Number of crossings in a regular drawing of a complete bipartite graph where the vertex positions on each part equal the Farey series of order n.
Original entry on oeis.org
1, 7, 59, 275, 1949, 3971, 20333, 45705, 120899, 205233, 629761, 897707, 2334291, 3461329, 5516985, 8467899
Offset: 1
Cf.
A359690 (vertices),
A359692 (regions),
A359693 (edges),
A359694 (k-gons),
A005728,
A159065,
A331755,
A359654,
A358887,
A358883,
A006842,
A006843.
A360043
Number of edges in a Farey fan of order n.
Original entry on oeis.org
4, 9, 18, 30, 52, 74, 112, 154, 210, 268, 352, 436, 552, 668, 802, 948, 1134, 1316, 1546, 1778, 2038, 2306, 2630, 2952, 3326, 3704, 4124, 4556, 5060, 5552, 6126, 6710, 7338, 7978, 8674, 9376, 10174, 10972, 11824, 12692, 13664, 14620, 15690, 16768, 17898, 19048, 20314, 21574, 22944, 24312
Offset: 1
- McIlroy, M. D. "A Note on Discrete Representation of Lines". AT&T Technical Journal, 64 (1985), 481-490.
Showing 1-7 of 7 results.
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